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The effect of low gravity during solidification on primary and secondary dendrite spacings is investigated. Dendritic spacing data for iron-carbon-type alloys and superalloys which were directionally solidified during aircraft low-g trajectories are examined. The low-g data data are compared with data for metal model materials and binary alloys, and theoretical models to explain the dendritic spacing are considered.
This paper presents a mathematical model for directional solidification of a binary alloy including a dendritic region underlying an all-liquid region. It is assumed initially that there exists a nonconvecting state with planar isotherms and isoconcentrates solidifying at a constant velocity. The stability of this system has been analyzed and nonlinear calculations are performed that show the effect of convection in the solidification process when the system is unstable. Results of calculations for various cases defined by the initial temperature gradient at the dendrite tips and varying strength of the gravitational field are presented for systems involving lead-tin alloys. The results show that the systems are stable for a gravitational constant of 0.0001 g(0) and that convection can be suppressed by appropriate choice of the container's size for higher values of the gravitational constant. It is also concluded that for the lead-tin systems considered, convection in the mushy zone is not significant below the upper 20 percent of the dendritic zone, if al all.
The Isothermal Dendritic Growth Experiment, which is expected to fly on the Space Shuttle to study dendritic solidification of molten metals such as iron and aluminum, is examined. Succinonitrile and pivalic acid are substitued for metals to permit visualiztion of dendritic growth. The technical features of the apparatus are described, including temperature control, the photographic system, and slow scan television. The teleoperations techniques for the experiment are discussed in detail.
Recent developments in the theory of pattern formation in dendritic crystal growth and viscous fingering in fluids are reviewed. Consideration is given to the discovery that weak capillary forces act as singular perturbations which lead to selection mechanisms in dendritic crystal growth and fingering patterns. Other topics include the conventional thermodynamic model of the solidification of a pure substance from its melt, fingering instability, pattern selection, the solvability theory, dendritic growth rates, the bubble effect discovered by Couder et al. (1986), the dynamics of pattern-forming systems, and snowflake formation.
The signal feedback process at the edge of the dendrite tip is investigated, and the global instability mechanism of the system is derived. A mechanism is developed to describe a discrete set of unstable global modes for the system. Called WEASR, the method considers the wave emission at the turning point and signal reflections between the turning point and the front edge of the tip. It is shown that the method can obtain the asymptotic solutions for the unstable global modes and the quantum condition for the corresponding eigenvalues. A turning point called the pattern formation condition is shown to be crucial in the formation of dendritic structure and the choice of the final tip velocity. The wave emission process is outlined, and the importance of a signal feedback process at the edge of the dendrite tip is demonstrated. Parameters such as stability and surface tension can be analyzed in terms of their effects on WEASR modes.
The line-of-sight averaged, time-dependent dendrite tip concentrations for the diffusion dominated vertical directional solidification of a metal model (ammonium chloride and water) were obtained by extrapolating exponentially fit diffusion layer profiles measured using a laser interferometer. The tip concentrations were shown to increase linearly with time throughout the diffusion dominated growth process for an initially stagnant dendritic array. The process was terminated for the cases chosen by convective breakdown suffered when the conditionally stable diffusion layer exceeded the critical Rayleigh criteria. The transient tip concentrations were determined to significantly exceed the values predicted for steady state, thus producing much larger constitutional undercoolings. This has ramifications for growth speeds, arm spacings and the dendritic structure itself.
The Isothermal Dendritic Growth Experiment (IDGE) has been designed to provide microgravity data on dendritic growth for a critical test of theory. This paper updates progress on constructing a crystal growth chamber suitable for space flight. The IDGE chamber is constructed from glass and stainless steel and is hermetically sealed by electron beam welds and glass-metal seals. Initial tests of the chambers sample's melting point plateau show that the new chamber design is capable of preserving the 99.9995 percent purity of succinonitrile. Dendrite growth can be initiated in the center of the IDGE chamber by means of thermo-electric coolers and a capillary injector tube (stinger). The new IDGE chamber is ready for fully integrated tests with the prototype IDGE engineering hardware at NASA's Lewis Research Center.
The NASA Isothermal Dendritic Growth Experiment (IDGE), which is to be performed on three of the U.S. Microgravity Payload flights, is discussed. IDGE is designed to investigate dendritic growth under microgravity. The theory of dendritic growth and the effects of gravity on it are reviewed, and the IDGE experimental apparatus, design, and ground-based tests are discussed.
The Isothermal Dendritic Growth Experiment (IDGE) flew on STS-62 to study the microscopic, tree-like structures (dendrites) that form within metals as they solidify from molten materials. The size, shape, and orientation of these dendrites affect the strength and usefulness of metals. Data from this experiment will be used to test and improve the mathematical models that support the industrial production of metals.
We measured dendritic tip velocities in pure succinonitrile (SCN) in microgravity. using a sequence of telemetered binary images sent to Earth from the Space Shuttle Columbia (STS-62). Growth velocities were measured as a function of the supercooling over the range 0.05-1.5 K. Microgravity observations show that buoyancy-induced convection alters the growth kinetics of SCN dendrites at supercooling as high as 1.3 K. Also, the dendrite velocity data measured under microgravity agree well with the Ivantsov paraboloidal diffusion solution when coupled to a scaling constant of sigma(sup *) = 0.0157.
It is generally accepted that liquid agitation during alloy solidification assists in crystal multiplication, as in dendrite fragmentation and the detachment of side arms in the mushy region of a casting. Even without deliberate stirring by electromagnetic or mechanical means, there is often vigorous interdendritic fluid flow promoted by natural thermosolutal convection. In this analysis, we shall estimate the stress at the root of a secondary dendrite arm of aluminum arising from the action of a flow of molten metal past the dendrite arm.
Recent observations of the disorder-order transition for colloidal hard spheres under microgravity revealed dendritic crystallites roughly 1-2 mm in size for samples in the coexistence region of the phase diagram. Order-of-magnitude estimates rationalize the absence of large or dendritic crystals under normal gravity and their stability to annealing in microgravity. A linear stability analysis of the Ackerson and Schaetzel model for crystallization of hard spheres establishes the domain of instability for diffusion-limited growth at small supersaturations. The relationship between hard-sphere and molecular crystal growth is established and exploited to relate the predicted linear instability to the well-developed dendrites observed.
In previous work, we found approximate solutions for paraboloids having perturbations with four-fold axial symmetry in order to model dendritic growth in cubic materials. These solutions provide self-consistent corrections through second order in a shape parameter e to the Peclet number-supercooling relation of the Ivantsov solution. The parameter e is proportional to the amplitude of the four-fold correction to the dendrite shape, as measured from the Ivantsov paraboloid of revolution. We calculate e by comparing the dendrite tip shape to the portion of the equilibrium shape near the growth direction, (001), for anisotropic surface free energy, where the ni are components of the unit normal of the crystal surface. This comparison results in epsilon = -2(epsilon 4), independent of the Peclet number. From the experimental value of epsilon 4, we find epsilon approximately 0.011, in good agreement with the measured value epsilon approximately 0.008 of LaCombe et al.
The RIDGE effort continues the aegis of the earlier, NASA-sponsored, Isothermal Dendritic Growth Experiment (IDGE) series of experiments through the continued analysis of microgravity data acquired during these earlier space flights. The preliminary observations presented here demonstrate that there are significant differences between SCN and the more anisotropic PVA dendrites. The side branch structure becomes amplified only further behind the tip, and the interface shape is generally wider (i.e. more hyperbolic than parabolic) in PVA than in SCN. These characteristics are seen to affect the process of heat transport. Additionally, the dendrites grown during the fourth United States Microgravity Payload (USMP-4) exhibit time-dependent growth characteristics and may not always have reached steady-state growth during the experiment.
A stagnant film model of the effects of thermosolutal convection on free dendritic growth of alloys is developed, and its predictions are compared to available earth-based experimental data for succinonitrileacetone alloys. It is found that the convection model gives excellent agreement with the measured dendrite tip velocities and radii for low solute concentrations. However, at higher solute concentrations the present predictions show some deviations from the measured data, and the measured (thermal) Peclet numbers tend to fall even below the predictions from diffusion theory. Furthermore, the measured selection parameter (sigma*) is significantly above the expected value of 0.02 and exhibits strong scatter. It is shown that convection is not responsible for these discrepancies. Some of the deviations between the predicted and measured data at higher supercoolings could be caused by measurement difficulties. The systematic disagreement in the selection parameter for higher solute concentrations and all supercoolings examined, indicates that the theory for the selection of the dendrite tip operating state in alloys may need to be reexamined.
The Pb-2.2 wt pct Sb alloy has been directionally solidified in 1-, 2-, 3-, and 7-mm-diameter crucibles with planar and dendritic liquid-solid interface orphology. For plane front solidification, the experimentally observed macrosegregation along the solidified length follows the relationship proposed by Favier. Application of a 0.4 T transverse magnetic field has no effect on the extent of convection. Reducing the ampoule diameter appears to decrease the extent of convection. However, extensive convection is still present even in the 1-mm-diameter crucible. An extrapolation of the observed behavior indicated that nearly diffusive transport conditions require ampoules that are about 40 microns in diameter. Reduction of the crucible diameter does not appear to have any significant effect on the primary dendrite spacing. However, it results in considerable distortion of the dendrite morphology and ordering. This is especially true for the 1-mm diameter samples.
As part of the Pore Formation and Mobility Investigation (PFMI), Succinonitrile Water alloys consisting of aligned dendritic arrays were re-melted prior to conducting directional solidification experiments in the microgravity environment aboard the International Space Station. Thermocapillary convection initiated by bubbles at the solid-liquid interface during controlled melt back of the alloy was observed to disrupt the initial dendritic alignment. Disruption ranged from detaching large arrays to the transport of small dendrite fragments at the interface. The role of bubble size and origin is discussed along with subsequent consequences upon reinitiating controlled solidification.
The primary dendrite trunk diameters of Al-Si alloys that were directionally solidified over a range of processing conditions have been measured. These data are analyzed with a model based primarily on an assessment of secondary dendrite arm dissolution in the mushy zone. Good fit with the experimental data is seen and it is suggested that the primary dendrite trunk diameter is a useful metric that correlates well with the actual solidification processing parameters. These results are placed in context with the limited results from the aluminium - 7 wt. % silicon samples directionally solidified aboard the International Space Station as part of the MICAST project.